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1 vote
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116 views

Do Gromov hyperbolic spaces admit concical geodesic bicombings?

Consider a metric space $(X,d)$ with a distinguished selection of geodesics, i.e. a geodesic bicombing $\sigma:X\times X\times [0,1]\rightarrow X$. We call a geodesic bicombing conical if it ...
4 votes
0 answers
114 views

"Snowflaked" Hausdorff metric

Let $(X,d_X)$ be a compact metric space and let $Comp(X)$ be the set of closed subsets of $X$ with the Hausdorff metric: $$ D(A,B)\overset{\text{def}}{=} \, \max\left\{\sup_{b\in B}\,d_{A}(b),\sup_{a\...
0 votes
0 answers
81 views

Gromov–Hausdorff closure of non-positively curved graphs

Setup: Let $\Gamma$ be the set of non-positively curved weighted connected graphs, with finitely many points, which are isometrically embedded in $\mathbb{R}^n$; for some $n\in \mathbb{N}$;$n\geq 2$. ...
5 votes
1 answer
200 views

Criterion for Kuratowski Limit Inferior

Let $(X,d_X)$ be a compact metric space and let $\{K_n\}_{n=1}^{\infty}$ be a collection of non-empty compact subsets. Let $K\subseteq X$ be compact. Then, if for every $x_n \in K_n$ we have $$ d_X(...